1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_COST_SCALING_H |
---|
20 | #define LEMON_COST_SCALING_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow_algs |
---|
23 | /// \file |
---|
24 | /// \brief Cost scaling algorithm for finding a minimum cost flow. |
---|
25 | |
---|
26 | #include <vector> |
---|
27 | #include <deque> |
---|
28 | #include <limits> |
---|
29 | |
---|
30 | #include <lemon/core.h> |
---|
31 | #include <lemon/maps.h> |
---|
32 | #include <lemon/math.h> |
---|
33 | #include <lemon/adaptors.h> |
---|
34 | #include <lemon/circulation.h> |
---|
35 | #include <lemon/bellman_ford.h> |
---|
36 | |
---|
37 | namespace lemon { |
---|
38 | |
---|
39 | /// \addtogroup min_cost_flow_algs |
---|
40 | /// @{ |
---|
41 | |
---|
42 | /// \brief Implementation of the cost scaling algorithm for finding a |
---|
43 | /// minimum cost flow. |
---|
44 | /// |
---|
45 | /// \ref CostScaling implements the cost scaling algorithm performing |
---|
46 | /// augment/push and relabel operations for finding a minimum cost |
---|
47 | /// flow. |
---|
48 | /// |
---|
49 | /// \tparam Digraph The digraph type the algorithm runs on. |
---|
50 | /// \tparam LowerMap The type of the lower bound map. |
---|
51 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
---|
52 | /// \tparam CostMap The type of the cost (length) map. |
---|
53 | /// \tparam SupplyMap The type of the supply map. |
---|
54 | /// |
---|
55 | /// \warning |
---|
56 | /// - Arc capacities and costs should be \e non-negative \e integers. |
---|
57 | /// - Supply values should be \e signed \e integers. |
---|
58 | /// - The value types of the maps should be convertible to each other. |
---|
59 | /// - \c CostMap::Value must be signed type. |
---|
60 | /// |
---|
61 | /// \note Arc costs are multiplied with the number of nodes during |
---|
62 | /// the algorithm so overflow problems may arise more easily than with |
---|
63 | /// other minimum cost flow algorithms. |
---|
64 | /// If it is available, <tt>long long int</tt> type is used instead of |
---|
65 | /// <tt>long int</tt> in the inside computations. |
---|
66 | /// |
---|
67 | /// \author Peter Kovacs |
---|
68 | template < typename Digraph, |
---|
69 | typename LowerMap = typename Digraph::template ArcMap<int>, |
---|
70 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
---|
71 | typename CostMap = typename Digraph::template ArcMap<int>, |
---|
72 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
---|
73 | class CostScaling |
---|
74 | { |
---|
75 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
76 | |
---|
77 | typedef typename CapacityMap::Value Capacity; |
---|
78 | typedef typename CostMap::Value Cost; |
---|
79 | typedef typename SupplyMap::Value Supply; |
---|
80 | typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap; |
---|
81 | typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap; |
---|
82 | |
---|
83 | typedef ResidualDigraph< const Digraph, |
---|
84 | CapacityArcMap, CapacityArcMap > ResDigraph; |
---|
85 | typedef typename ResDigraph::Arc ResArc; |
---|
86 | |
---|
87 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
---|
88 | typedef long long int LCost; |
---|
89 | #else |
---|
90 | typedef long int LCost; |
---|
91 | #endif |
---|
92 | typedef typename Digraph::template ArcMap<LCost> LargeCostMap; |
---|
93 | |
---|
94 | public: |
---|
95 | |
---|
96 | /// The type of the flow map. |
---|
97 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
---|
98 | /// The type of the potential map. |
---|
99 | typedef typename Digraph::template NodeMap<LCost> PotentialMap; |
---|
100 | |
---|
101 | private: |
---|
102 | |
---|
103 | /// \brief Map adaptor class for handling residual arc costs. |
---|
104 | /// |
---|
105 | /// Map adaptor class for handling residual arc costs. |
---|
106 | template <typename Map> |
---|
107 | class ResidualCostMap : public MapBase<ResArc, typename Map::Value> |
---|
108 | { |
---|
109 | private: |
---|
110 | |
---|
111 | const Map &_cost_map; |
---|
112 | |
---|
113 | public: |
---|
114 | |
---|
115 | ///\e |
---|
116 | ResidualCostMap(const Map &cost_map) : |
---|
117 | _cost_map(cost_map) {} |
---|
118 | |
---|
119 | ///\e |
---|
120 | inline typename Map::Value operator[](const ResArc &e) const { |
---|
121 | return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
---|
122 | } |
---|
123 | |
---|
124 | }; //class ResidualCostMap |
---|
125 | |
---|
126 | /// \brief Map adaptor class for handling reduced arc costs. |
---|
127 | /// |
---|
128 | /// Map adaptor class for handling reduced arc costs. |
---|
129 | class ReducedCostMap : public MapBase<Arc, LCost> |
---|
130 | { |
---|
131 | private: |
---|
132 | |
---|
133 | const Digraph &_gr; |
---|
134 | const LargeCostMap &_cost_map; |
---|
135 | const PotentialMap &_pot_map; |
---|
136 | |
---|
137 | public: |
---|
138 | |
---|
139 | ///\e |
---|
140 | ReducedCostMap( const Digraph &gr, |
---|
141 | const LargeCostMap &cost_map, |
---|
142 | const PotentialMap &pot_map ) : |
---|
143 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
---|
144 | |
---|
145 | ///\e |
---|
146 | inline LCost operator[](const Arc &e) const { |
---|
147 | return _cost_map[e] + _pot_map[_gr.source(e)] |
---|
148 | - _pot_map[_gr.target(e)]; |
---|
149 | } |
---|
150 | |
---|
151 | }; //class ReducedCostMap |
---|
152 | |
---|
153 | private: |
---|
154 | |
---|
155 | // The digraph the algorithm runs on |
---|
156 | const Digraph &_graph; |
---|
157 | // The original lower bound map |
---|
158 | const LowerMap *_lower; |
---|
159 | // The modified capacity map |
---|
160 | CapacityArcMap _capacity; |
---|
161 | // The original cost map |
---|
162 | const CostMap &_orig_cost; |
---|
163 | // The scaled cost map |
---|
164 | LargeCostMap _cost; |
---|
165 | // The modified supply map |
---|
166 | SupplyNodeMap _supply; |
---|
167 | bool _valid_supply; |
---|
168 | |
---|
169 | // Arc map of the current flow |
---|
170 | FlowMap *_flow; |
---|
171 | bool _local_flow; |
---|
172 | // Node map of the current potentials |
---|
173 | PotentialMap *_potential; |
---|
174 | bool _local_potential; |
---|
175 | |
---|
176 | // The residual cost map |
---|
177 | ResidualCostMap<LargeCostMap> _res_cost; |
---|
178 | // The residual digraph |
---|
179 | ResDigraph *_res_graph; |
---|
180 | // The reduced cost map |
---|
181 | ReducedCostMap *_red_cost; |
---|
182 | // The excess map |
---|
183 | SupplyNodeMap _excess; |
---|
184 | // The epsilon parameter used for cost scaling |
---|
185 | LCost _epsilon; |
---|
186 | // The scaling factor |
---|
187 | int _alpha; |
---|
188 | |
---|
189 | public: |
---|
190 | |
---|
191 | /// \brief General constructor (with lower bounds). |
---|
192 | /// |
---|
193 | /// General constructor (with lower bounds). |
---|
194 | /// |
---|
195 | /// \param digraph The digraph the algorithm runs on. |
---|
196 | /// \param lower The lower bounds of the arcs. |
---|
197 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
198 | /// \param cost The cost (length) values of the arcs. |
---|
199 | /// \param supply The supply values of the nodes (signed). |
---|
200 | CostScaling( const Digraph &digraph, |
---|
201 | const LowerMap &lower, |
---|
202 | const CapacityMap &capacity, |
---|
203 | const CostMap &cost, |
---|
204 | const SupplyMap &supply ) : |
---|
205 | _graph(digraph), _lower(&lower), _capacity(digraph), _orig_cost(cost), |
---|
206 | _cost(digraph), _supply(digraph), _flow(NULL), _local_flow(false), |
---|
207 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
---|
208 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
---|
209 | { |
---|
210 | // Check the sum of supply values |
---|
211 | Supply sum = 0; |
---|
212 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
---|
213 | _valid_supply = sum == 0; |
---|
214 | |
---|
215 | for (ArcIt e(_graph); e != INVALID; ++e) _capacity[e] = capacity[e]; |
---|
216 | for (NodeIt n(_graph); n != INVALID; ++n) _supply[n] = supply[n]; |
---|
217 | |
---|
218 | // Remove non-zero lower bounds |
---|
219 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
220 | if (lower[e] != 0) { |
---|
221 | _capacity[e] -= lower[e]; |
---|
222 | _supply[_graph.source(e)] -= lower[e]; |
---|
223 | _supply[_graph.target(e)] += lower[e]; |
---|
224 | } |
---|
225 | } |
---|
226 | } |
---|
227 | /* |
---|
228 | /// \brief General constructor (without lower bounds). |
---|
229 | /// |
---|
230 | /// General constructor (without lower bounds). |
---|
231 | /// |
---|
232 | /// \param digraph The digraph the algorithm runs on. |
---|
233 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
234 | /// \param cost The cost (length) values of the arcs. |
---|
235 | /// \param supply The supply values of the nodes (signed). |
---|
236 | CostScaling( const Digraph &digraph, |
---|
237 | const CapacityMap &capacity, |
---|
238 | const CostMap &cost, |
---|
239 | const SupplyMap &supply ) : |
---|
240 | _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
---|
241 | _cost(digraph), _supply(supply), _flow(NULL), _local_flow(false), |
---|
242 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
---|
243 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
---|
244 | { |
---|
245 | // Check the sum of supply values |
---|
246 | Supply sum = 0; |
---|
247 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
---|
248 | _valid_supply = sum == 0; |
---|
249 | } |
---|
250 | |
---|
251 | /// \brief Simple constructor (with lower bounds). |
---|
252 | /// |
---|
253 | /// Simple constructor (with lower bounds). |
---|
254 | /// |
---|
255 | /// \param digraph The digraph the algorithm runs on. |
---|
256 | /// \param lower The lower bounds of the arcs. |
---|
257 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
258 | /// \param cost The cost (length) values of the arcs. |
---|
259 | /// \param s The source node. |
---|
260 | /// \param t The target node. |
---|
261 | /// \param flow_value The required amount of flow from node \c s |
---|
262 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
263 | CostScaling( const Digraph &digraph, |
---|
264 | const LowerMap &lower, |
---|
265 | const CapacityMap &capacity, |
---|
266 | const CostMap &cost, |
---|
267 | Node s, Node t, |
---|
268 | Supply flow_value ) : |
---|
269 | _graph(digraph), _lower(&lower), _capacity(capacity), _orig_cost(cost), |
---|
270 | _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
271 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
---|
272 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
---|
273 | { |
---|
274 | // Remove non-zero lower bounds |
---|
275 | _supply[s] = flow_value; |
---|
276 | _supply[t] = -flow_value; |
---|
277 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
278 | if (lower[e] != 0) { |
---|
279 | _capacity[e] -= lower[e]; |
---|
280 | _supply[_graph.source(e)] -= lower[e]; |
---|
281 | _supply[_graph.target(e)] += lower[e]; |
---|
282 | } |
---|
283 | } |
---|
284 | _valid_supply = true; |
---|
285 | } |
---|
286 | |
---|
287 | /// \brief Simple constructor (without lower bounds). |
---|
288 | /// |
---|
289 | /// Simple constructor (without lower bounds). |
---|
290 | /// |
---|
291 | /// \param digraph The digraph the algorithm runs on. |
---|
292 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
293 | /// \param cost The cost (length) values of the arcs. |
---|
294 | /// \param s The source node. |
---|
295 | /// \param t The target node. |
---|
296 | /// \param flow_value The required amount of flow from node \c s |
---|
297 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
298 | CostScaling( const Digraph &digraph, |
---|
299 | const CapacityMap &capacity, |
---|
300 | const CostMap &cost, |
---|
301 | Node s, Node t, |
---|
302 | Supply flow_value ) : |
---|
303 | _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost), |
---|
304 | _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
305 | _potential(NULL), _local_potential(false), _res_cost(_cost), |
---|
306 | _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0) |
---|
307 | { |
---|
308 | _supply[s] = flow_value; |
---|
309 | _supply[t] = -flow_value; |
---|
310 | _valid_supply = true; |
---|
311 | } |
---|
312 | */ |
---|
313 | /// Destructor. |
---|
314 | ~CostScaling() { |
---|
315 | if (_local_flow) delete _flow; |
---|
316 | if (_local_potential) delete _potential; |
---|
317 | delete _res_graph; |
---|
318 | delete _red_cost; |
---|
319 | } |
---|
320 | |
---|
321 | /// \brief Set the flow map. |
---|
322 | /// |
---|
323 | /// Set the flow map. |
---|
324 | /// |
---|
325 | /// \return \c (*this) |
---|
326 | CostScaling& flowMap(FlowMap &map) { |
---|
327 | if (_local_flow) { |
---|
328 | delete _flow; |
---|
329 | _local_flow = false; |
---|
330 | } |
---|
331 | _flow = ↦ |
---|
332 | return *this; |
---|
333 | } |
---|
334 | |
---|
335 | /// \brief Set the potential map. |
---|
336 | /// |
---|
337 | /// Set the potential map. |
---|
338 | /// |
---|
339 | /// \return \c (*this) |
---|
340 | CostScaling& potentialMap(PotentialMap &map) { |
---|
341 | if (_local_potential) { |
---|
342 | delete _potential; |
---|
343 | _local_potential = false; |
---|
344 | } |
---|
345 | _potential = ↦ |
---|
346 | return *this; |
---|
347 | } |
---|
348 | |
---|
349 | /// \name Execution control |
---|
350 | |
---|
351 | /// @{ |
---|
352 | |
---|
353 | /// \brief Run the algorithm. |
---|
354 | /// |
---|
355 | /// Run the algorithm. |
---|
356 | /// |
---|
357 | /// \param partial_augment By default the algorithm performs |
---|
358 | /// partial augment and relabel operations in the cost scaling |
---|
359 | /// phases. Set this parameter to \c false for using local push and |
---|
360 | /// relabel operations instead. |
---|
361 | /// |
---|
362 | /// \return \c true if a feasible flow can be found. |
---|
363 | bool run(bool partial_augment = true) { |
---|
364 | if (partial_augment) { |
---|
365 | return init() && startPartialAugment(); |
---|
366 | } else { |
---|
367 | return init() && startPushRelabel(); |
---|
368 | } |
---|
369 | } |
---|
370 | |
---|
371 | /// @} |
---|
372 | |
---|
373 | /// \name Query Functions |
---|
374 | /// The result of the algorithm can be obtained using these |
---|
375 | /// functions.\n |
---|
376 | /// \ref lemon::CostScaling::run() "run()" must be called before |
---|
377 | /// using them. |
---|
378 | |
---|
379 | /// @{ |
---|
380 | |
---|
381 | /// \brief Return a const reference to the arc map storing the |
---|
382 | /// found flow. |
---|
383 | /// |
---|
384 | /// Return a const reference to the arc map storing the found flow. |
---|
385 | /// |
---|
386 | /// \pre \ref run() must be called before using this function. |
---|
387 | const FlowMap& flowMap() const { |
---|
388 | return *_flow; |
---|
389 | } |
---|
390 | |
---|
391 | /// \brief Return a const reference to the node map storing the |
---|
392 | /// found potentials (the dual solution). |
---|
393 | /// |
---|
394 | /// Return a const reference to the node map storing the found |
---|
395 | /// potentials (the dual solution). |
---|
396 | /// |
---|
397 | /// \pre \ref run() must be called before using this function. |
---|
398 | const PotentialMap& potentialMap() const { |
---|
399 | return *_potential; |
---|
400 | } |
---|
401 | |
---|
402 | /// \brief Return the flow on the given arc. |
---|
403 | /// |
---|
404 | /// Return the flow on the given arc. |
---|
405 | /// |
---|
406 | /// \pre \ref run() must be called before using this function. |
---|
407 | Capacity flow(const Arc& arc) const { |
---|
408 | return (*_flow)[arc]; |
---|
409 | } |
---|
410 | |
---|
411 | /// \brief Return the potential of the given node. |
---|
412 | /// |
---|
413 | /// Return the potential of the given node. |
---|
414 | /// |
---|
415 | /// \pre \ref run() must be called before using this function. |
---|
416 | Cost potential(const Node& node) const { |
---|
417 | return (*_potential)[node]; |
---|
418 | } |
---|
419 | |
---|
420 | /// \brief Return the total cost of the found flow. |
---|
421 | /// |
---|
422 | /// Return the total cost of the found flow. The complexity of the |
---|
423 | /// function is \f$ O(e) \f$. |
---|
424 | /// |
---|
425 | /// \pre \ref run() must be called before using this function. |
---|
426 | Cost totalCost() const { |
---|
427 | Cost c = 0; |
---|
428 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
429 | c += (*_flow)[e] * _orig_cost[e]; |
---|
430 | return c; |
---|
431 | } |
---|
432 | |
---|
433 | /// @} |
---|
434 | |
---|
435 | private: |
---|
436 | |
---|
437 | /// Initialize the algorithm. |
---|
438 | bool init() { |
---|
439 | if (!_valid_supply) return false; |
---|
440 | // The scaling factor |
---|
441 | _alpha = 8; |
---|
442 | |
---|
443 | // Initialize flow and potential maps |
---|
444 | if (!_flow) { |
---|
445 | _flow = new FlowMap(_graph); |
---|
446 | _local_flow = true; |
---|
447 | } |
---|
448 | if (!_potential) { |
---|
449 | _potential = new PotentialMap(_graph); |
---|
450 | _local_potential = true; |
---|
451 | } |
---|
452 | |
---|
453 | _red_cost = new ReducedCostMap(_graph, _cost, *_potential); |
---|
454 | _res_graph = new ResDigraph(_graph, _capacity, *_flow); |
---|
455 | |
---|
456 | // Initialize the scaled cost map and the epsilon parameter |
---|
457 | Cost max_cost = 0; |
---|
458 | int node_num = countNodes(_graph); |
---|
459 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
460 | _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha; |
---|
461 | if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e]; |
---|
462 | } |
---|
463 | _epsilon = max_cost * node_num; |
---|
464 | |
---|
465 | // Find a feasible flow using Circulation |
---|
466 | Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap, |
---|
467 | SupplyMap > |
---|
468 | circulation( _graph, constMap<Arc>(Capacity(0)), _capacity, |
---|
469 | _supply ); |
---|
470 | return circulation.flowMap(*_flow).run(); |
---|
471 | } |
---|
472 | |
---|
473 | /// Execute the algorithm performing partial augmentation and |
---|
474 | /// relabel operations. |
---|
475 | bool startPartialAugment() { |
---|
476 | // Paramters for heuristics |
---|
477 | // const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
---|
478 | // const int BF_HEURISTIC_BOUND_FACTOR = 3; |
---|
479 | // Maximum augment path length |
---|
480 | const int MAX_PATH_LENGTH = 4; |
---|
481 | |
---|
482 | // Variables |
---|
483 | typename Digraph::template NodeMap<Arc> pred_arc(_graph); |
---|
484 | typename Digraph::template NodeMap<bool> forward(_graph); |
---|
485 | typename Digraph::template NodeMap<OutArcIt> next_out(_graph); |
---|
486 | typename Digraph::template NodeMap<InArcIt> next_in(_graph); |
---|
487 | typename Digraph::template NodeMap<bool> next_dir(_graph); |
---|
488 | std::deque<Node> active_nodes; |
---|
489 | std::vector<Node> path_nodes; |
---|
490 | |
---|
491 | // int node_num = countNodes(_graph); |
---|
492 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
493 | 1 : _epsilon / _alpha ) |
---|
494 | { |
---|
495 | /* |
---|
496 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
---|
497 | // to check if the current flow is optimal |
---|
498 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
---|
499 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
---|
500 | ShiftCostMap shift_cost(_res_cost, 1); |
---|
501 | BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
---|
502 | bf.init(0); |
---|
503 | bool done = false; |
---|
504 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
---|
505 | for (int i = 0; i < K && !done; ++i) |
---|
506 | done = bf.processNextWeakRound(); |
---|
507 | if (done) break; |
---|
508 | } |
---|
509 | */ |
---|
510 | // Saturate arcs not satisfying the optimality condition |
---|
511 | Capacity delta; |
---|
512 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
513 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
514 | delta = _capacity[e] - (*_flow)[e]; |
---|
515 | _excess[_graph.source(e)] -= delta; |
---|
516 | _excess[_graph.target(e)] += delta; |
---|
517 | (*_flow)[e] = _capacity[e]; |
---|
518 | } |
---|
519 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
---|
520 | _excess[_graph.target(e)] -= (*_flow)[e]; |
---|
521 | _excess[_graph.source(e)] += (*_flow)[e]; |
---|
522 | (*_flow)[e] = 0; |
---|
523 | } |
---|
524 | } |
---|
525 | |
---|
526 | // Find active nodes (i.e. nodes with positive excess) |
---|
527 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
528 | if (_excess[n] > 0) active_nodes.push_back(n); |
---|
529 | } |
---|
530 | |
---|
531 | // Initialize the next arc maps |
---|
532 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
533 | next_out[n] = OutArcIt(_graph, n); |
---|
534 | next_in[n] = InArcIt(_graph, n); |
---|
535 | next_dir[n] = true; |
---|
536 | } |
---|
537 | |
---|
538 | // Perform partial augment and relabel operations |
---|
539 | while (active_nodes.size() > 0) { |
---|
540 | // Select an active node (FIFO selection) |
---|
541 | if (_excess[active_nodes[0]] <= 0) { |
---|
542 | active_nodes.pop_front(); |
---|
543 | continue; |
---|
544 | } |
---|
545 | Node start = active_nodes[0]; |
---|
546 | path_nodes.clear(); |
---|
547 | path_nodes.push_back(start); |
---|
548 | |
---|
549 | // Find an augmenting path from the start node |
---|
550 | Node u, tip = start; |
---|
551 | LCost min_red_cost; |
---|
552 | while ( _excess[tip] >= 0 && |
---|
553 | int(path_nodes.size()) <= MAX_PATH_LENGTH ) |
---|
554 | { |
---|
555 | if (next_dir[tip]) { |
---|
556 | for (OutArcIt e = next_out[tip]; e != INVALID; ++e) { |
---|
557 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
558 | u = _graph.target(e); |
---|
559 | pred_arc[u] = e; |
---|
560 | forward[u] = true; |
---|
561 | next_out[tip] = e; |
---|
562 | tip = u; |
---|
563 | path_nodes.push_back(tip); |
---|
564 | goto next_step; |
---|
565 | } |
---|
566 | } |
---|
567 | next_dir[tip] = false; |
---|
568 | } |
---|
569 | for (InArcIt e = next_in[tip]; e != INVALID; ++e) { |
---|
570 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
---|
571 | u = _graph.source(e); |
---|
572 | pred_arc[u] = e; |
---|
573 | forward[u] = false; |
---|
574 | next_in[tip] = e; |
---|
575 | tip = u; |
---|
576 | path_nodes.push_back(tip); |
---|
577 | goto next_step; |
---|
578 | } |
---|
579 | } |
---|
580 | |
---|
581 | // Relabel tip node |
---|
582 | min_red_cost = std::numeric_limits<LCost>::max() / 2; |
---|
583 | for (OutArcIt oe(_graph, tip); oe != INVALID; ++oe) { |
---|
584 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
---|
585 | (*_red_cost)[oe] < min_red_cost ) |
---|
586 | min_red_cost = (*_red_cost)[oe]; |
---|
587 | } |
---|
588 | for (InArcIt ie(_graph, tip); ie != INVALID; ++ie) { |
---|
589 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
---|
590 | min_red_cost = -(*_red_cost)[ie]; |
---|
591 | } |
---|
592 | (*_potential)[tip] -= min_red_cost + _epsilon; |
---|
593 | |
---|
594 | // Reset the next arc maps |
---|
595 | next_out[tip] = OutArcIt(_graph, tip); |
---|
596 | next_in[tip] = InArcIt(_graph, tip); |
---|
597 | next_dir[tip] = true; |
---|
598 | |
---|
599 | // Step back |
---|
600 | if (tip != start) { |
---|
601 | path_nodes.pop_back(); |
---|
602 | tip = path_nodes[path_nodes.size()-1]; |
---|
603 | } |
---|
604 | |
---|
605 | next_step: |
---|
606 | continue; |
---|
607 | } |
---|
608 | |
---|
609 | // Augment along the found path (as much flow as possible) |
---|
610 | Capacity delta; |
---|
611 | for (int i = 1; i < int(path_nodes.size()); ++i) { |
---|
612 | u = path_nodes[i]; |
---|
613 | delta = forward[u] ? |
---|
614 | _capacity[pred_arc[u]] - (*_flow)[pred_arc[u]] : |
---|
615 | (*_flow)[pred_arc[u]]; |
---|
616 | delta = std::min(delta, _excess[path_nodes[i-1]]); |
---|
617 | (*_flow)[pred_arc[u]] += forward[u] ? delta : -delta; |
---|
618 | _excess[path_nodes[i-1]] -= delta; |
---|
619 | _excess[u] += delta; |
---|
620 | if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u); |
---|
621 | } |
---|
622 | } |
---|
623 | } |
---|
624 | |
---|
625 | // Compute node potentials for the original costs |
---|
626 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
---|
627 | BellmanFord< ResDigraph, ResidualCostMap<CostMap> > |
---|
628 | bf(*_res_graph, res_cost); |
---|
629 | bf.init(0); bf.start(); |
---|
630 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
631 | (*_potential)[n] = bf.dist(n); |
---|
632 | |
---|
633 | // Handle non-zero lower bounds |
---|
634 | if (_lower) { |
---|
635 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
636 | (*_flow)[e] += (*_lower)[e]; |
---|
637 | } |
---|
638 | return true; |
---|
639 | } |
---|
640 | |
---|
641 | /// Execute the algorithm performing push and relabel operations. |
---|
642 | bool startPushRelabel() { |
---|
643 | // Paramters for heuristics |
---|
644 | // const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
---|
645 | // const int BF_HEURISTIC_BOUND_FACTOR = 3; |
---|
646 | |
---|
647 | typename Digraph::template NodeMap<bool> hyper(_graph, false); |
---|
648 | typename Digraph::template NodeMap<Arc> pred_arc(_graph); |
---|
649 | typename Digraph::template NodeMap<bool> forward(_graph); |
---|
650 | typename Digraph::template NodeMap<OutArcIt> next_out(_graph); |
---|
651 | typename Digraph::template NodeMap<InArcIt> next_in(_graph); |
---|
652 | typename Digraph::template NodeMap<bool> next_dir(_graph); |
---|
653 | std::deque<Node> active_nodes; |
---|
654 | |
---|
655 | // int node_num = countNodes(_graph); |
---|
656 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
657 | 1 : _epsilon / _alpha ) |
---|
658 | { |
---|
659 | /* |
---|
660 | // "Early Termination" heuristic: use Bellman-Ford algorithm |
---|
661 | // to check if the current flow is optimal |
---|
662 | if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
---|
663 | typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap; |
---|
664 | ShiftCostMap shift_cost(_res_cost, 1); |
---|
665 | BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost); |
---|
666 | bf.init(0); |
---|
667 | bool done = false; |
---|
668 | int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num)); |
---|
669 | for (int i = 0; i < K && !done; ++i) |
---|
670 | done = bf.processNextWeakRound(); |
---|
671 | if (done) break; |
---|
672 | } |
---|
673 | */ |
---|
674 | |
---|
675 | // Saturate arcs not satisfying the optimality condition |
---|
676 | Capacity delta; |
---|
677 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
678 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
679 | delta = _capacity[e] - (*_flow)[e]; |
---|
680 | _excess[_graph.source(e)] -= delta; |
---|
681 | _excess[_graph.target(e)] += delta; |
---|
682 | (*_flow)[e] = _capacity[e]; |
---|
683 | } |
---|
684 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
---|
685 | _excess[_graph.target(e)] -= (*_flow)[e]; |
---|
686 | _excess[_graph.source(e)] += (*_flow)[e]; |
---|
687 | (*_flow)[e] = 0; |
---|
688 | } |
---|
689 | } |
---|
690 | |
---|
691 | // Find active nodes (i.e. nodes with positive excess) |
---|
692 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
693 | if (_excess[n] > 0) active_nodes.push_back(n); |
---|
694 | } |
---|
695 | |
---|
696 | // Initialize the next arc maps |
---|
697 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
698 | next_out[n] = OutArcIt(_graph, n); |
---|
699 | next_in[n] = InArcIt(_graph, n); |
---|
700 | next_dir[n] = true; |
---|
701 | } |
---|
702 | |
---|
703 | // Perform push and relabel operations |
---|
704 | while (active_nodes.size() > 0) { |
---|
705 | // Select an active node (FIFO selection) |
---|
706 | Node n = active_nodes[0], t; |
---|
707 | bool relabel_enabled = true; |
---|
708 | |
---|
709 | // Perform push operations if there are admissible arcs |
---|
710 | if (_excess[n] > 0 && next_dir[n]) { |
---|
711 | OutArcIt e = next_out[n]; |
---|
712 | for ( ; e != INVALID; ++e) { |
---|
713 | if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) { |
---|
714 | delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]); |
---|
715 | t = _graph.target(e); |
---|
716 | |
---|
717 | // Push-look-ahead heuristic |
---|
718 | Capacity ahead = -_excess[t]; |
---|
719 | for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) { |
---|
720 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
---|
721 | ahead += _capacity[oe] - (*_flow)[oe]; |
---|
722 | } |
---|
723 | for (InArcIt ie(_graph, t); ie != INVALID; ++ie) { |
---|
724 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
---|
725 | ahead += (*_flow)[ie]; |
---|
726 | } |
---|
727 | if (ahead < 0) ahead = 0; |
---|
728 | |
---|
729 | // Push flow along the arc |
---|
730 | if (ahead < delta) { |
---|
731 | (*_flow)[e] += ahead; |
---|
732 | _excess[n] -= ahead; |
---|
733 | _excess[t] += ahead; |
---|
734 | active_nodes.push_front(t); |
---|
735 | hyper[t] = true; |
---|
736 | relabel_enabled = false; |
---|
737 | break; |
---|
738 | } else { |
---|
739 | (*_flow)[e] += delta; |
---|
740 | _excess[n] -= delta; |
---|
741 | _excess[t] += delta; |
---|
742 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
743 | active_nodes.push_back(t); |
---|
744 | } |
---|
745 | |
---|
746 | if (_excess[n] == 0) break; |
---|
747 | } |
---|
748 | } |
---|
749 | if (e != INVALID) { |
---|
750 | next_out[n] = e; |
---|
751 | } else { |
---|
752 | next_dir[n] = false; |
---|
753 | } |
---|
754 | } |
---|
755 | |
---|
756 | if (_excess[n] > 0 && !next_dir[n]) { |
---|
757 | InArcIt e = next_in[n]; |
---|
758 | for ( ; e != INVALID; ++e) { |
---|
759 | if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) { |
---|
760 | delta = std::min((*_flow)[e], _excess[n]); |
---|
761 | t = _graph.source(e); |
---|
762 | |
---|
763 | // Push-look-ahead heuristic |
---|
764 | Capacity ahead = -_excess[t]; |
---|
765 | for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) { |
---|
766 | if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0) |
---|
767 | ahead += _capacity[oe] - (*_flow)[oe]; |
---|
768 | } |
---|
769 | for (InArcIt ie(_graph, t); ie != INVALID; ++ie) { |
---|
770 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0) |
---|
771 | ahead += (*_flow)[ie]; |
---|
772 | } |
---|
773 | if (ahead < 0) ahead = 0; |
---|
774 | |
---|
775 | // Push flow along the arc |
---|
776 | if (ahead < delta) { |
---|
777 | (*_flow)[e] -= ahead; |
---|
778 | _excess[n] -= ahead; |
---|
779 | _excess[t] += ahead; |
---|
780 | active_nodes.push_front(t); |
---|
781 | hyper[t] = true; |
---|
782 | relabel_enabled = false; |
---|
783 | break; |
---|
784 | } else { |
---|
785 | (*_flow)[e] -= delta; |
---|
786 | _excess[n] -= delta; |
---|
787 | _excess[t] += delta; |
---|
788 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
789 | active_nodes.push_back(t); |
---|
790 | } |
---|
791 | |
---|
792 | if (_excess[n] == 0) break; |
---|
793 | } |
---|
794 | } |
---|
795 | next_in[n] = e; |
---|
796 | } |
---|
797 | |
---|
798 | // Relabel the node if it is still active (or hyper) |
---|
799 | if (relabel_enabled && (_excess[n] > 0 || hyper[n])) { |
---|
800 | LCost min_red_cost = std::numeric_limits<LCost>::max() / 2; |
---|
801 | for (OutArcIt oe(_graph, n); oe != INVALID; ++oe) { |
---|
802 | if ( _capacity[oe] - (*_flow)[oe] > 0 && |
---|
803 | (*_red_cost)[oe] < min_red_cost ) |
---|
804 | min_red_cost = (*_red_cost)[oe]; |
---|
805 | } |
---|
806 | for (InArcIt ie(_graph, n); ie != INVALID; ++ie) { |
---|
807 | if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost) |
---|
808 | min_red_cost = -(*_red_cost)[ie]; |
---|
809 | } |
---|
810 | (*_potential)[n] -= min_red_cost + _epsilon; |
---|
811 | hyper[n] = false; |
---|
812 | |
---|
813 | // Reset the next arc maps |
---|
814 | next_out[n] = OutArcIt(_graph, n); |
---|
815 | next_in[n] = InArcIt(_graph, n); |
---|
816 | next_dir[n] = true; |
---|
817 | } |
---|
818 | |
---|
819 | // Remove nodes that are not active nor hyper |
---|
820 | while ( active_nodes.size() > 0 && |
---|
821 | _excess[active_nodes[0]] <= 0 && |
---|
822 | !hyper[active_nodes[0]] ) { |
---|
823 | active_nodes.pop_front(); |
---|
824 | } |
---|
825 | } |
---|
826 | } |
---|
827 | |
---|
828 | // Compute node potentials for the original costs |
---|
829 | ResidualCostMap<CostMap> res_cost(_orig_cost); |
---|
830 | BellmanFord< ResDigraph, ResidualCostMap<CostMap> > |
---|
831 | bf(*_res_graph, res_cost); |
---|
832 | bf.init(0); bf.start(); |
---|
833 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
834 | (*_potential)[n] = bf.dist(n); |
---|
835 | |
---|
836 | // Handle non-zero lower bounds |
---|
837 | if (_lower) { |
---|
838 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
839 | (*_flow)[e] += (*_lower)[e]; |
---|
840 | } |
---|
841 | return true; |
---|
842 | } |
---|
843 | |
---|
844 | }; //class CostScaling |
---|
845 | |
---|
846 | ///@} |
---|
847 | |
---|
848 | } //namespace lemon |
---|
849 | |
---|
850 | #endif //LEMON_COST_SCALING_H |
---|